Let $$A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr } } \right)$, ($\alpha $ $ \in $ R) such that ${A^{32}} = \left( {\matrix{ 0 & { - 1} \cr 1 & 0 \cr } } \right)$ then a value of $\alpha $$ is

Question

Let $$A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr } } \right)$, ($\alpha $ $ \in $ R)
such that ${A^{32}} = \left( {\matrix{ 0 & { - 1} \cr 1 & 0 \cr } } \right)$ then a value of $\alpha $$ is

${\pi \over {16}}$

${\pi \over {32}}$

${\pi \over {64}}$

Solution

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